View Full Version : Setting constants like hbar to unity
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\n\n\nMany systems of units are often defined by setting assorted constants\nto unity:\n\nAtomic units: m = e = hbar = 1\nNatural units: hbar = c = 1\nGeometrized units: G = c = 1\nPlanck units: hbar = G = c = 1\n\nWhen I first saw equations like the ones above, I thought that they\nwere just lazy ways of writing\n\nm = 1 mass unit,\ne = 1 electric charge unit,\n\net cetera. However, judging from Appendix F in R.M. Wald\'s "General\nRelativity" or Appendix F in Burcham & Jobes\' "Nuclear and Particle\nPhysics", particle physicists and general relativists really do mean\nexactly what they write. Appendices like those discuss which\ndimensions become equal when constants are set to unity. Thus, the\nabove equations really do mean that the entire physical constant, as\nopposed to just its numerical value, is set to 1.\n\nOr so I thought until I, less than an hour ago, reread Duff, Okun &\nVeneziano\'s discussion of how many truly fundamental constants there\nare.\n\nhttp://www.arxiv.org/abs/physics/0110060\n\nThere, in section "5. The art of putting c = 1, hbar = 1, G = 1", L.B.\nOkun claims that these expressions are not genuine equalities and that\nthey should not be taken too literally.\n\nSo what is the status of the above equations? What do they really\nmean? Is Okun wrong?\n\n(I understand that constants can be made to disappear from fundamental\nequations through clever changes of variables. E.g., a cleverly chosen\nfactor b will transform the Schrödinger equation for psi(x,t) to an\nequation in terms of the field phi(s,t) = psi(bs,t). That equation\nlooks exactly like the simplified version of the Schrödinger equation\nthat could obtained if the equation m = e = hbar = 1 were taken\nliterally. Perhaps m = e = hbar = 1 is just the instruction "make the\nchanges of variables that make m, e, and hbar disappear!", rather than\na statement that m, e, and hbar are all equal to each other and to 1?\nBut then it\'s difficult to make sense of Wald\'s appendix F and Burcham\n& Jobes\' appendix F...)\n\nErik\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Many systems of units are often defined by setting assorted constants
to unity:
Atomic units: m = e = \hbar = 1
Natural units: \hbar = c = 1
Geometrized units: G = c = 1
Planck units: \hbar = G = c = 1
When I first saw equations like the ones above, I thought that they
were just lazy ways of writing
m = 1 mass unit,
e = 1 electric charge unit,
et cetera. However, judging from Appendix F in R.M. Wald's "General
Relativity" or Appendix F in Burcham & Jobes' "Nuclear and Particle
Physics", particle physicists and general relativists really do mean
exactly what they write. Appendices like those discuss which
dimensions become equal when constants are set to unity. Thus, the
above equations really do mean that the entire physical constant, as
opposed to just its numerical value, is set to 1.
Or so I thought until I, less than an hour ago, reread Duff, Okun &
Veneziano's discussion of how many truly fundamental constants there
are.
http://www.arxiv.org/abs/http://www.arxiv.org/abs/physics/0110060
There, in section "5. The art of putting c = 1, \hbar = 1, G = 1", L.B.
Okun claims that these expressions are not genuine equalities and that
they should not be taken too literally.
So what is the status of the above equations? What do they really
mean? Is Okun wrong?
(I understand that constants can be made to disappear from fundamental
equations through clever changes of variables. E.g., a cleverly chosen
factor b will transform the Schrödinger equation for \psi(x,t) to an
equation in terms of the field \phi(s,t) = \psi(bs,t). That equation
looks exactly like the simplified version of the Schrödinger equation
that could obtained if the equation m = e = \hbar = 1 were taken
literally. Perhaps m = e = \hbar = 1 is just the instruction "make the
changes of variables that make m, e, and \hbar disappear!", rather than
a statement that m, e, and \hbar are all equal to each other and to 1?
But then it's difficult to make sense of Wald's appendix F and Burcham
& Jobes' appendix F...)
Erik
Cl.Massé
Aug14-04, 06:58 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n"Erik" <erite423@yahoo.se> a écrit dans le message de\nnews:d018ba78.0408121117.7ed5b760@posting.goog le.com...\n\n> Many systems of units are often defined by setting assorted constants\n> to unity:\n>\n> Atomic units: m = e = hbar = 1\n> Natural units: hbar = c = 1\n> Geometrized units: G = c = 1\n> Planck units: hbar = G = c = 1\n\n> However, judging from Appendix F in R.M. Wald\'s "General\n> Relativity" or Appendix F in Burcham & Jobes\' "Nuclear and Particle\n> Physics", particle physicists and general relativists really do mean\n> exactly what they write. Appendices like those discuss which\n> dimensions become equal when constants are set to unity. Thus, the\n> above equations really do mean that the entire physical constant, as\n> opposed to just its numerical value, is set to 1.\n\nSome physical theories just says two concepts are identical. For\ninstance, special relativity says time is the same as space; quantum\nmechanics says time is the same as reciprocal energy (so that energy is\nthe same as momentum). We have two dimensional units only from\nhistorical reasons. If we had two different dimensional units for\nheight and width, we could set their ratio to 1 without changing any\nphysical content. It is merely the operation of using the same unit for\nboth.\nThere are 4 basic dimensional units, so with 3 universal constants, they\nreduce to 1. We so follow the intended course of physics: unification.\nThe ultimate theory has the formidable task of explaining and giving a\nfundamental standard for the remaining dimension.\n\n--\n~~~~ clmasse on free dot F-country\nLiberty, Equality, Profitability.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>"Erik" <erite423@yahoo.se> a écrit dans le message de
news:d018ba78.0408121117.7ed5b760@posting.google.c om...
> Many systems of units are often defined by setting assorted constants
> to unity:
>
> Atomic units: m = e = \hbar = 1
> Natural units: \hbar = c = 1
> Geometrized units: G = c = 1
> Planck units: \hbar = G = c = 1
> However, judging from Appendix F in R.M. Wald's "General
> Relativity" or Appendix F in Burcham & Jobes' "Nuclear and Particle
> Physics", particle physicists and general relativists really do mean
> exactly what they write. Appendices like those discuss which
> dimensions become equal when constants are set to unity. Thus, the
> above equations really do mean that the entire physical constant, as
> opposed to just its numerical value, is set to 1.
Some physical theories just says two concepts are identical. For
instance, special relativity says time is the same as space; quantum
mechanics says time is the same as reciprocal energy (so that energy is
the same as momentum). We have two dimensional units only from
historical reasons. If we had two different dimensional units for
height and width, we could set their ratio to 1 without changing any
physical content. It is merely the operation of using the same unit for
both.
There are 4 basic dimensional units, so with 3 universal constants, they
reduce to 1. We so follow the intended course of physics: unification.
The ultimate theory has the formidable task of explaining and giving a
fundamental standard for the remaining dimension.
--
~~~~ clmasse on free dot F-country
Liberty, Equality, Profitability.
greywolf42
Aug14-04, 06:58 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\n"Erik" <erite423@yahoo.se> wrote in message\nnews:d018ba78.0408121117.7ed5b760@posting .google.com...\n>\n> Many systems of units are often defined by setting assorted constants\n> to unity:\n>\n> Atomic units: m = e = hbar = 1\n> Natural units: hbar = c = 1\n> Geometrized units: G = c = 1\n> Planck units: hbar = G = c = 1\n>\n> When I first saw equations like the ones above, I thought that they\n> were just lazy ways of writing\n>\n> m = 1 mass unit,\n> e = 1 electric charge unit,\n>\n> et cetera. However, judging from Appendix F in R.M. Wald\'s "General\n> Relativity" or Appendix F in Burcham & Jobes\' "Nuclear and Particle\n> Physics", particle physicists and general relativists really do mean\n> exactly what they write. Appendices like those discuss which\n> dimensions become equal when constants are set to unity. Thus, the\n> above equations really do mean that the entire physical constant, as\n> opposed to just its numerical value, is set to 1.\n>\n> Or so I thought until I, less than an hour ago, reread Duff, Okun &\n> Veneziano\'s discussion of how many truly fundamental constants there\n> are.\n>\n> http://www.arxiv.org/abs/physics/0110060\n>\n> There, in section "5. The art of putting c = 1, hbar = 1, G = 1", L.B.\n> Okun claims that these expressions are not genuine equalities and that\n> they should not be taken too literally.\n>\n> So what is the status of the above equations? What do they really\n> mean? Is Okun wrong?\n>\n> (I understand that constants can be made to disappear from fundamental\n> equations through clever changes of variables. E.g., a cleverly chosen\n> factor b will transform the Schrödinger equation for psi(x,t) to an\n> equation in terms of the field phi(s,t) = psi(bs,t). That equation\n> looks exactly like the simplified version of the Schrödinger equation\n> that could obtained if the equation m = e = hbar = 1 were taken\n> literally. Perhaps m = e = hbar = 1 is just the instruction "make the\n> changes of variables that make m, e, and hbar disappear!", rather than\n> a statement that m, e, and hbar are all equal to each other and to 1?\n> But then it\'s difficult to make sense of Wald\'s appendix F and Burcham\n> & Jobes\' appendix F...)\n\nThe *unit* = 1 convention is simply a rather sloppy timesaver. Any student\nof elementary physics that provided a value without a corresponding set of\nunits gets the answer marked wrong.\n\nHowever, if the convention (no matter how sloppy) is explicitly stated and\nunderstood, it does not itself cause problems (so long as you put the \'real\'\nunits and conversion constants in, just before calculating the answer).\nIt\'s only when one actually starts believing that it has a physical meaning\nthat the problems arise. This is especially a risk in the geometric\ninterpretation of GR. One can conveniently ignore the fact that one of the\nfour equivalent dimensions in spacetime is really a different concept. This\nis the risk of all shortcuts. That one forgets why one started doing\nsomething.\n\n--\ngreywolf42\nubi dubium ibi libertas\n{remove planet for e-mail}\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>"Erik" <erite423@yahoo.se> wrote in message
news:d018ba78.0408121117.7ed5b760@posting.google.c om...
>
> Many systems of units are often defined by setting assorted constants
> to unity:
>
> Atomic units: m = e = \hbar = 1
> Natural units: \hbar = c = 1
> Geometrized units: G = c = 1
> Planck units: \hbar = G = c = 1
>
> When I first saw equations like the ones above, I thought that they
> were just lazy ways of writing
>
> m = 1 mass unit,
> e = 1 electric charge unit,
>
> et cetera. However, judging from Appendix F in R.M. Wald's "General
> Relativity" or Appendix F in Burcham & Jobes' "Nuclear and Particle
> Physics", particle physicists and general relativists really do mean
> exactly what they write. Appendices like those discuss which
> dimensions become equal when constants are set to unity. Thus, the
> above equations really do mean that the entire physical constant, as
> opposed to just its numerical value, is set to 1.
>
> Or so I thought until I, less than an hour ago, reread Duff, Okun &
> Veneziano's discussion of how many truly fundamental constants there
> are.
>
> http://www.arxiv.org/abs/http://www.arxiv.org/abs/physics/0110060
>
> There, in section "5. The art of putting c = 1, \hbar = 1, G = 1", L.B.
> Okun claims that these expressions are not genuine equalities and that
> they should not be taken too literally.
>
> So what is the status of the above equations? What do they really
> mean? Is Okun wrong?
>
> (I understand that constants can be made to disappear from fundamental
> equations through clever changes of variables. E.g., a cleverly chosen
> factor b will transform the Schrödinger equation for \psi(x,t) to an
> equation in terms of the field \phi(s,t) = \psi(bs,t). That equation
> looks exactly like the simplified version of the Schrödinger equation
> that could obtained if the equation m = e = \hbar = 1 were taken
> literally. Perhaps m = e = \hbar = 1 is just the instruction "make the
> changes of variables that make m, e, and \hbar disappear!", rather than
> a statement that m, e, and \hbar are all equal to each other and to 1?
> But then it's difficult to make sense of Wald's appendix F and Burcham
> & Jobes' appendix F...)
The *unit* = 1 convention is simply a rather sloppy timesaver. Any student
of elementary physics that provided a value without a corresponding set of
units gets the answer marked wrong.
However, if the convention (no matter how sloppy) is explicitly stated and
understood, it does not itself cause problems (so long as you put the 'real'
units and conversion constants in, just before calculating the answer).
It's only when one actually starts believing that it has a physical meaning
that the problems arise. This is especially a risk in the geometric
interpretation of GR. One can conveniently ignore the fact that one of the
four equivalent dimensions in spacetime is really a different concept. This
is the risk of all shortcuts. That one forgets why one started doing
something.
--
greywolf42
ubi dubium ibi libertas
{remove planet for e-mail}
Doug Sweetser
Aug16-04, 12:55 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\n\ngreywolf42 wrote:\n\n> The *unit* = 1 convention is simply a rather sloppy timesaver. Any\n> student of elementary physics that provided a value without a\n> corresponding set of units gets the answer marked wrong.\n\nFeynman was an old-timer who didn\'t like the c=1 convention, I believe\non sloppiness grounds (he certainly understood what people were\ndoing :-) I do like to keep all my units because they help indicate\nwhat catagory of physics one is dealing with. Classical physics does\nnot have c or h. The constant G is a calling card of gravity.\nNewton\'s scalar field theory is classical because it has no c or h.\nThe Schwarzschild metric that is a particular solution to Einstein\'s\nfield equations has a G and a c, so this is a relativistic approach to\ngravity. A relativistic quantum gravity theory would have G, c, and h.\nThis is one reason for the focus on the Planck length which equals\n((h/2 pi) G/c^3)^(1/2).\n\n\ndoug\nquaternions.com\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>greywolf42 wrote:
> The *unit* = 1 convention is simply a rather sloppy timesaver. Any
> student of elementary physics that provided a value without a
> corresponding set of units gets the answer marked wrong.
Feynman was an old-timer who didn't like the c=1 convention, I believe
on sloppiness grounds (he certainly understood what people were
doing :-) I do like to keep all my units because they help indicate
what catagory of physics one is dealing with. Classical physics does
not have c or h. The constant G is a calling card of gravity.
Newton's scalar field theory is classical because it has no c or h.
The Schwarzschild metric that is a particular solution to Einstein's
field equations has a G and a c, so this is a relativistic approach to
gravity. A relativistic quantum gravity theory would have G, c, and h.
This is one reason for the focus on the Planck length which equals
((h/2 \pi) G/c^3)^(1/2).
doug
quaternions.com
J. J. Lodder
Aug16-04, 12:55 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\n\ngreywolf42 <mingstb@marssim-ss.com> wrote:\n\n> However, if the convention (no matter how sloppy) is explicitly stated and\n> understood, it does not itself cause problems (so long as you put the \'real\'\n> units and conversion constants in, just before calculating the answer).\n> It\'s only when one actually starts believing that it has a physical meaning\n> that the problems arise. This is especially a risk in the geometric\n> interpretation of GR. One can conveniently ignore the fact that one of the\n> four equivalent dimensions in spacetime is really a different concept. This\n> is the risk of all shortcuts. That one forgets why one started doing\n> something.\n\nAnd that \'forgetting\' is a good thing.\nTake a historical example:\n200 years ago people generally believed that heat (the caloric fluid)\nand work (force times distance) were quite different things, physically,\nand they used different units to measure them.\nIt was a great discovery (Joule and all that, among others)\nthat the two are manifestations the same thing, energy,\nand that there exists a fundamental constant relating the two.\n(which we call in modern terminology 4.2 Joule/calory)\n\nNowadays (excepting some food faddists and perhaps the always backwards\nAmericans) the calories have been nearly forgotten.\nPeople even dare to give the amount of heat in joules,\ninstead of in the \'real\' unit of heat.\n\nIt is a matter of historical accident only that we are stuck with a\n\'fundamental constant\' called c, of value 299 792 458 m/s.\nWere it possible to redefine our unit system without regard for backward\ncompatibility we wouldn\'t have a c, or a separate unit of length.\nAnd our descendants 200 years hence (historians of science excepted)\nmight be blisfullly unaware that different units for space and time\never existed.\n\nBut alas, the metric system came too early,\nand it is too late to change again,\n\nJan\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>greywolf42 <mingstb@marssim-ss.com> wrote:
> However, if the convention (no matter how sloppy) is explicitly stated and
> understood, it does not itself cause problems (so long as you put the 'real'
> units and conversion constants in, just before calculating the answer).
> It's only when one actually starts believing that it has a physical meaning
> that the problems arise. This is especially a risk in the geometric
> interpretation of GR. One can conveniently ignore the fact that one of the
> four equivalent dimensions in spacetime is really a different concept. This
> is the risk of all shortcuts. That one forgets why one started doing
> something.
And that 'forgetting' is a good thing.
Take a historical example:
200 years ago people generally believed that heat (the caloric fluid)
and work (force times distance) were quite different things, physically,
and they used different units to measure them.
It was a great discovery (Joule and all that, among others)
that the two are manifestations the same thing, energy,
and that there exists a fundamental constant relating the two.
(which we call in modern terminology 4.2 Joule/calory)
Nowadays (excepting some food faddists and perhaps the always backwards
Americans) the calories have been nearly forgotten.
People even dare to give the amount of heat in joules,
instead of in the 'real' unit of heat.
It is a matter of historical accident only that we are stuck with a
'fundamental constant' called c, of value 299 792 458 m/s.
Were it possible to redefine our unit system without regard for backward
compatibility we wouldn't have a c, or a separate unit of length.
And our descendants 200 years hence (historians of science excepted)
might be blisfullly unaware that different units for space and time
ever existed.
But alas, the metric system came too early,
and it is too late to change again,
Jan
J. J. Lodder
Aug16-04, 12:56 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\nErik <erite423@yahoo.se> wrote:\n\n> Many systems of units are often defined by setting assorted constants\n> to unity:\n>=20\n> Atomic units: m =3D e =3D hbar =3D 1\n> Natural units: hbar =3D c =3D 1\n> Geometrized units: G =3D c =3D 1\n> Planck units: hbar =3D G =3D c =3D 1\n\nMore precisely: by choosing units such that they are 1\n(Meaning have the value 1)\n\n> When I first saw equations like the ones above, I thought that they\n> were just lazy ways of writing\n>=20\n> m =3D 1 mass unit,\n> e =3D 1 electric charge unit,\n>=20\n> et cetera. However, judging from Appendix F in R.M. Wald\'s "General\n> Relativity" or Appendix F in Burcham & Jobes\' "Nuclear and Particle\n> Physics", particle physicists and general relativists really do mean\n> exactly what they write.=20\n\nOf course, what else did you expect? This is physics.\n\n> Appendices like those discuss which\n> dimensions become equal when constants are set to unity. Thus, the\n> above equations really do mean that the entire physical constant, as\n> opposed to just its numerical value, is set to 1.\n\nIndeed, an often made choice is to have c =3D 1 and dimensionless.\n\n> Or so I thought until I, less than an hour ago, reread Duff, Okun &\n> Veneziano\'s discussion of how many truly fundamental constants there\n> are.\n>=20\n> http://www.arxiv.org/abs/physics/0110060\n>=20\n> There, in section "5. The art of putting c =3D 1, hbar =3D 1, G =3D 1",=\nL.B.\n> Okun claims that these expressions are not genuine equalities and that\n> they should not be taken too literally.\n\nOkun doesn\'t understand this game.\n\n> So what is the status of the above equations?\n\nThey define a system of units.\n\n> What do they really mean?\n\nThey have no \'real\' meaning, beyond defining a unit system.\nReality (by definition) doesn\'t depend on the unit system\nwe -choose- to describe it with.\n\n> Is Okun wrong?\n\nYes.\n\n> (I understand that constants can be made to disappear from fundamental\n> equations through clever changes of variables. E.g., a cleverly chosen\n> factor b will transform the Schr=F6dinger equation for psi(x,t) to an\n> equation in terms of the field phi(s,t) =3D psi(bs,t). That equation\n> looks exactly like the simplified version of the Schr=F6dinger equation\n> that could obtained if the equation m =3D e =3D hbar =3D 1 were taken\n> literally. Perhaps m =3D e =3D hbar =3D 1 is just the instruction "make=\nthe\n> changes of variables that make m, e, and hbar disappear!", rather than\n> a statement that m, e, and hbar are all equal to each other and to 1?\n\nThat amounts to the same thing, in practice.\n\n> But then it\'s difficult to make sense of Wald\'s appendix F and Burcham\n> & Jobes\' appendix F...)\n\nThe key to understanding this subject is that dimensions\ndo not have an objective existence.\nThey are human constructs, without relation to reality,\nto be chosen in any convenient way,\nsubject only to the requirement of consistency.\nAny consistent system of dimensions is as good as any other,\nalthough perhaps less useful for certain applications.\n\nIn particular, one can give c value 1, and dimension [I],\nor value 1, and dimension [L]/[T],\nwhichever may be convenient for a particular application.\n\nA often used compromise is to have c =3D 1,\nand to write it nevertheless in final results,\nas in for example m_{top} =3D 175 GeV/c^2.\n\nBest,\n\nJan\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Erik <erite423@yahoo.se> wrote:
> Many systems of units are often defined by setting assorted constants
> to unity:
>=20
> Atomic units: m =3D e =3D \hbar =3D 1
> Natural units: \hbar =3D c =3D 1
> Geometrized units: G =3D c =3D 1
> Planck units: \hbar =3D G =3D c =3D 1
More precisely: by choosing units such that they are 1
(Meaning have the value 1)
> When I first saw equations like the ones above, I thought that they
> were just lazy ways of writing
>=20
> m =3D 1 mass unit,
> e =3D 1 electric charge unit,
>=20
> et cetera. However, judging from Appendix F in R.M. Wald's "General
> Relativity" or Appendix F in Burcham & Jobes' "Nuclear and Particle
> Physics", particle physicists and general relativists really do mean
> exactly what they write.=20
Of course, what else did you expect? This is physics.
> Appendices like those discuss which
> dimensions become equal when constants are set to unity. Thus, the
> above equations really do mean that the entire physical constant, as
> opposed to just its numerical value, is set to 1.
Indeed, an often made choice is to have c =3D 1 and dimensionless.
> Or so I thought until I, less than an hour ago, reread Duff, Okun &
> Veneziano's discussion of how many truly fundamental constants there
> are.
>=20
> http://www.arxiv.org/abs/http://www.arxiv.org/abs/physics/0110060
>=20
> There, in section "5. The art of putting c =3D 1, \hbar =3D 1, G =3D 1",=
L.B.
> Okun claims that these expressions are not genuine equalities and that
> they should not be taken too literally.
Okun doesn't understand this game.
> So what is the status of the above equations?
They define a system of units.
> What do they really mean?
They have no 'real' meaning, beyond defining a unit system.
Reality (by definition) doesn't depend on the unit system
we -choose- to describe it with.
> Is Okun wrong?
Yes.
> (I understand that constants can be made to disappear from fundamental
> equations through clever changes of variables. E.g., a cleverly chosen
> factor b will transform the Schr=F6dinger equation for \psi(x,t) to an
> equation in terms of the field \phi(s,t) =3D \psi(bs,t). That equation
> looks exactly like the simplified version of the Schr=F6dinger equation
> that could obtained if the equation m =3D e =3D \hbar =3D 1 were taken
> literally. Perhaps m =3D e =3D \hbar =3D 1 is just the instruction "make=
the
> changes of variables that make m, e, and \hbar disappear!", rather than
> a statement that m, e, and \hbar are all equal to each other and to 1?
That amounts to the same thing, in practice.
> But then it's difficult to make sense of Wald's appendix F and Burcham
> & Jobes' appendix F...)
The key to understanding this subject is that dimensions
do not have an objective existence.
They are human constructs, without relation to reality,
to be chosen in any convenient way,
subject only to the requirement of consistency.
Any consistent system of dimensions is as good as any other,
although perhaps less useful for certain applications.
In particular, one can give c value 1, and dimension [I],
or value 1, and dimension [L]/[T],
whichever may be convenient for a particular application.
A often used compromise is to have c =3D 1,
and to write it nevertheless in final results,
as in for example m_{top} =3D 175 GeV/c^2.
Best,
Jan
greywolf42
Aug17-04, 11:26 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\n"Doug Sweetser" <sweetser@alum.mit.edu> wrote in message\nnews:cfntr2\\$qjt\\$1@pcls4.std.com...\n> \n> greywolf42 wrote:\n>\n> > The *unit* = 1 convention is simply a rather sloppy timesaver. Any\n> > student of elementary physics that provided a value without a\n> > corresponding set of units gets the answer marked wrong.\n>\n> Feynman was an old-timer who didn\'t like the c=1 convention, I believe\n> on sloppiness grounds (he certainly understood what people were\n> doing :-) I do like to keep all my units because they help indicate\n> what catagory of physics one is dealing with.\n\nThat\'s certainly a good use of information.\n\n> Classical physics does not have c or h.\n\n??? Maxwells equations certainly have \'c\'. And that\'s as classical as you\ncan get. One can obtain "h" as the classical action term for Maxwell\'s\nequations ... in Maxwell\'s fluid model. (By using it, you avoid the pure\nmathematicians\'s \'ultraviolet catastrophe.\')\n\n> The constant G is a calling card of gravity.\n> Newton\'s scalar field theory is classical because it has no c or h.\n> The Schwarzschild metric that is a particular solution to Einstein\'s\n> field equations has a G and a c, so this is a relativistic approach to\n> gravity. A relativistic quantum gravity theory would have G, c, and h.\n> This is one reason for the focus on the Planck length which equals\n> ((h/2 pi) G/c^3)^(1/2).\n\n--\ngreywolf42\nubi dubium ibi libertas\n{remove planet for e-mail}\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>"Doug Sweetser" <sweetser@alum.mit.edu> wrote in message
news:cfntr2$qjt$1@pcls4.std.com...
>
> greywolf42 wrote:
>
> > The *unit* = 1 convention is simply a rather sloppy timesaver. Any
> > student of elementary physics that provided a value without a
> > corresponding set of units gets the answer marked wrong.
>
> Feynman was an old-timer who didn't like the c=1 convention, I believe
> on sloppiness grounds (he certainly understood what people were
> doing :-) I do like to keep all my units because they help indicate
> what catagory of physics one is dealing with.
That's certainly a good use of information.
> Classical physics does not have c or h.
??? Maxwells equations certainly have 'c'. And that's as classical as you
can get. One can obtain "h" as the classical action term for Maxwell's
equations ... in Maxwell's fluid model. (By using it, you avoid the pure
mathematicians's 'ultraviolet catastrophe.')
> The constant G is a calling card of gravity.
> Newton's scalar field theory is classical because it has no c or h.
> The Schwarzschild metric that is a particular solution to Einstein's
> field equations has a G and a c, so this is a relativistic approach to
> gravity. A relativistic quantum gravity theory would have G, c, and h.
> This is one reason for the focus on the Planck length which equals
> ((h/2 \pi) G/c^3)^(1/2).
--
greywolf42
ubi dubium ibi libertas
{remove planet for e-mail}
robert bristow-johnson
Aug17-04, 11:27 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\n\n\nnospam@de-ster.demon.nl (J. J. Lodder) wrote in message news:<1gigomq.1kseudkcnww31N@de-ster.xs4all.nl>...\n> Erik <erite423@yahoo.se> wrote:\n>\n> > et cetera. However, judging from Appendix F in R.M. Wald\'s "General\n> > Relativity" or Appendix F in Burcham & Jobes\' "Nuclear and Particle\n> > Physics", particle physicists and general relativists really do mean\n> > exactly what they write.\n>\n> Of course, what else did you expect? This is physics.\n\noh c\'mon Jan, physikers are never nebulous about the concepts they\ndeal with?? i\'m only a lowly EE but as we move from Newton through\nEinstein, Heisenberg, Schrodinger, and on to quarks and eventually\nstrings, this thing gets more obscure by the minute (despite Green\'s\n"Elegant Universe").\n\n> > Appendices like those discuss which\n> > dimensions become equal when constants are set to unity. Thus, the\n> > above equations really do mean that the entire physical constant, as\n> > opposed to just its numerical value, is set to 1.\n>\n> Indeed, an often made choice is to have c = 1 and dimensionless.\n>\n> > Or so I thought until I, less than an hour ago, reread Duff, Okun &\n> > Veneziano\'s discussion of how many truly fundamental constants there\n> > are.\n> > There, in section "5. The art of putting c = 1, hbar = 1, G = 1", L.B.\n> > Okun claims that these expressions are not genuine equalities and that\n> > they should not be taken too literally.\n>\n> Okun doesn\'t understand this game.\n\nbut does he understand the *reality*? (as much as Duff and/or\nVeneziano?)\n\n>\n> > So what is the status of the above equations?\n>\n> They define a system of units.\n\na system of units that are totally non-anthropocentric. that is a\nvery special system of units that, it seems to me, that Nature prefers\nto express herself with.\n\n> > What do they really mean?\n>\n> They have no \'real\' meaning, beyond defining a unit system.\n> Reality (by definition) doesn\'t depend on the unit system\n> we -choose- to describe it with.\n\nbut, apart from little dimensionless factors (like 4*pi, i still think\nthat Planck should have set 4*pi*G to 1, or perhaps 8*pi*G to 1) that\npeople get to argue about, it isn\'t *we* who choose these Natural\nUnits. it\'s Nature. *we* only get to discover them\n\n> > Is Okun wrong?\n>\n> Yes.\n\nJan, it\'s difficult for a slug (i.e. elec. engr.) like me to decide\nwho to believe. you? Okun? Baez? Duff? Veneziano? all\nheavyweights. but Okun makes more natural sense to me on some stuff\n(i actually go further and Duff would call me a "partisan of the\n4-Constant Party" because i see electric charge as a distinct\ndimension of physical quantity apart from time, length, and mass) and\nDuff on other stuff (such as our inability to detect a change in a\ndimensionful constant since we always measure dimensionful quantities\nagainst some other like dimensioned standard).\n\n> > (I understand that constants can be made to disappear from fundamental\n> > equations through clever changes of variables. E.g., a cleverly chosen\n> > factor b will transform the Schrodinger equation for psi(x,t) to an\n> > equation in terms of the field phi(s,t) = psi(bs,t). That equation\n> > looks exactly like the simplified version of the Schrodinger equation\n> > that could obtained if the equation m = e = hbar = 1 were taken\n> > literally. Perhaps m = e = hbar = 1 is just the instruction "make the\n> > changes of variables that make m, e, and hbar disappear!", rather than\n> > a statement that m, e, and hbar are all equal to each other and to 1?\n>\n> That amounts to the same thing, in practice.\n\nthat i understand (and agree with).\n\n> > But then it\'s difficult to make sense of Wald\'s appendix F and Burcham\n> > & Jobes\' appendix F...)\n>\n> The key to understanding this subject is that dimensions\n> do not have an objective existence.\n\nboy, that\'s an existential statement!! why can\'t the same be said of\nany physical quantity?\n\n> They are human constructs,\n> without relation to reality,\n\nis not any/every physical theory? we humans construct a theory to\nattempt to describe what we observe (with whatever senses and\ninstruments we have) in what we think is reality. to say that force\nor mass is really there but the fundamental differentiation between\nquantities of time and length or mass or energy, that those\nfundamental distictions of "stuff" are not really there but are merely\nhuman constructs?? that\'s hard to swallow. (at least for engineering\nslugs.)\n\n> to be chosen in any convenient way,\n> subject only to the requirement of consistency.\n> Any consistent system of dimensions is as good as any other,\n\ni think the jury is still out on that verdict.\n\n> although perhaps less useful for certain applications.\n\nthat is true (at least IMHO).\n\n> In particular, one can give c value 1, and dimension [I],\n\ni dunno what [I] is.\n\n> or value 1, and dimension [L]/[T],\n> whichever may be convenient for a particular application.\n\ndimension is important to help check on errors. if you end up adding\n(or comparing) apples to oranges, it\'s a good idea to recheck your\nmaths. comparing(or summing) unlike dimensioned quantities is not\nphysically meaningful, at least to the neaderthal engineers.\n\n> A often used compromise is to have c = 1,\n> and to write it nevertheless in final results,\n> as in for example m_{top} = 175 GeV/c^2.\n\ni would think that once you set c=1, you better not stick it in later\nlest you replace some "1" somewhere with the wrong power of c by not\nkeeping track of it. the way to keep track is to leave it in there\nfrom the beginning. i mean, which is it? is it\n\nG(mu,nu) = 8*pi*G * T(mu,nu) ?\n\nor is it\n\nG(mu,nu) = 8*pi*G/c^4 * T(mu,nu) ?\n\nmaybe it\'s c^3 or c^2?\n\nsorry to be a thorn.\n\nregards,\n\nr b-j\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>nospam@de-ster.demon.nl (J. J. Lodder) wrote in message news:<1gigomq.1kseudkcnww31N@de-ster.xs4all.nl>...
> Erik <erite423@yahoo.se> wrote:
>
> > et cetera. However, judging from Appendix F in R.M. Wald's "General
> > Relativity" or Appendix F in Burcham & Jobes' "Nuclear and Particle
> > Physics", particle physicists and general relativists really do mean
> > exactly what they write.
>
> Of course, what else did you expect? This is physics.
oh c'mon Jan, physikers are never nebulous about the concepts they
deal with?? i'm only a lowly EE but as we move from Newton through
Einstein, Heisenberg, Schrodinger, and on to quarks and eventually
strings, this thing gets more obscure by the minute (despite Green's
"Elegant Universe").
> > Appendices like those discuss which
> > dimensions become equal when constants are set to unity. Thus, the
> > above equations really do mean that the entire physical constant, as
> > opposed to just its numerical value, is set to 1.
>
> Indeed, an often made choice is to have c = 1 and dimensionless.
>
> > Or so I thought until I, less than an hour ago, reread Duff, Okun &
> > Veneziano's discussion of how many truly fundamental constants there
> > are.
> > There, in section "5. The art of putting c = 1, \hbar = 1, G = 1", L.B.
> > Okun claims that these expressions are not genuine equalities and that
> > they should not be taken too literally.
>
> Okun doesn't understand this game.
but does he understand the *reality*? (as much as Duff and/or
Veneziano?)
>
> > So what is the status of the above equations?
>
> They define a system of units.
a system of units that are totally non-anthropocentric. that is a
very special system of units that, it seems to me, that Nature prefers
to express herself with.
> > What do they really mean?
>
> They have no 'real' meaning, beyond defining a unit system.
> Reality (by definition) doesn't depend on the unit system
> we -choose- to describe it with.
but, apart from little dimensionless factors (like 4*\pi, i still think
that Planck should have set 4*\pi*G to 1, or perhaps 8*\pi*G to 1) that
people get to argue about, it isn't *we* who choose these Natural
Units. it's Nature. *we* only get to discover them
> > Is Okun wrong?
>
> Yes.
Jan, it's difficult for a slug (i.e. elec. engr.) like me to decide
who to believe. you? Okun? Baez? Duff? Veneziano? all
heavyweights. but Okun makes more natural sense to me on some stuff
(i actually go further and Duff would call me a "partisan of the
4-Constant Party" because i see electric charge as a distinct
dimension of physical quantity apart from time, length, and mass) and
Duff on other stuff (such as our inability to detect a change in a
dimensionful constant since we always measure dimensionful quantities
against some other like dimensioned standard).
> > (I understand that constants can be made to disappear from fundamental
> > equations through clever changes of variables. E.g., a cleverly chosen
> > factor b will transform the Schrodinger equation for \psi(x,t) to an
> > equation in terms of the field \phi(s,t) = \psi(bs,t). That equation
> > looks exactly like the simplified version of the Schrodinger equation
> > that could obtained if the equation m = e = \hbar = 1 were taken
> > literally. Perhaps m = e = \hbar = 1 is just the instruction "make the
> > changes of variables that make m, e, and \hbar disappear!", rather than
> > a statement that m, e, and \hbar are all equal to each other and to 1?
>
> That amounts to the same thing, in practice.
that i understand (and agree with).
> > But then it's difficult to make sense of Wald's appendix F and Burcham
> > & Jobes' appendix F...)
>
> The key to understanding this subject is that dimensions
> do not have an objective existence.
boy, that's an existential statement!! why can't the same be said of
any physical quantity?
> They are human constructs,
> without relation to reality,
is not any/every physical theory? we humans construct a theory to
attempt to describe what we observe (with whatever senses and
instruments we have) in what we think is reality. to say that force
or mass is really there but the fundamental differentiation between
quantities of time and length or mass or energy, that those
fundamental distictions of "stuff" are not really there but are merely
human constructs?? that's hard to swallow. (at least for engineering
slugs.)
> to be chosen in any convenient way,
> subject only to the requirement of consistency.
> Any consistent system of dimensions is as good as any other,
i think the jury is still out on that verdict.
> although perhaps less useful for certain applications.
that is true (at least IMHO).
> In particular, one can give c value 1, and dimension [I],
i dunno what [I] is.
> or value 1, and dimension [L]/[T],
> whichever may be convenient for a particular application.
dimension is important to help check on errors. if you end up adding
(or comparing) apples to oranges, it's a good idea to recheck your
maths. comparing(or summing) unlike dimensioned quantities is not
physically meaningful, at least to the neaderthal engineers.
> A often used compromise is to have c = 1,
> and to write it nevertheless in final results,
> as in for example m_{top} = 175 GeV/c^2.
i would think that once you set c=1, you better not stick it in later
lest you replace some "1" somewhere with the wrong power of c by not
keeping track of it. the way to keep track is to leave it in there
from the beginning. i mean, which is it? is it
G(\mu,\nu) = 8*\pi*G * T(\mu,\nu) ?
or is it
G(\mu,\nu) = 8*\pi*G/c^4 * T(\mu,\nu) ?
maybe it's c^3 or c^2?
sorry to be a thorn.
regards,
r b-j
Frank Hellmann
Aug18-04, 04:08 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n> And our descendants 200 years hence (historians of science excepted)\n> might be blisfullly unaware that different units for space and time\n> ever existed.\n>\n> But alas, the metric system came too early,\n> and it is too late to change again,\n>\n\nUnlikely. The practical difference is just to great. For heat and\nenergy it doesn\'tmatter. Energy is never meassured directly. distances\nand times are, and with very different instruments.\nWhich is why, while in theoretical sciences it may make no conceptual\nsense to treat them with different units it certainly makes a lot of\nconceptual sense in experimental sciences where you have to treat them\nvery differently.\nTherefore they are here to stay, therefore the confussion and the need\nto translate them when going from a theoretically convenient system to\nan experimentally convenient system.\n\nThat said, I still would like to get a reference that seriously\nexplains the theoretically convenient modelland systematically\nexplores the origin of units.\n\nIt always seemed to me that the reason why we only need one unit is\nbecause the only important thing is how the individual variables\ncontribute to the Lagrangian which should be of [unit]^m.\nSo we can have m * v ^ 2 if [m] = [unit] and [length] = [time] =\n[unit] ^ n and if we want to get the right units for the harmonic\npotential m * x ^ 2 we get m = 2n + 1. We could have length and time\nunitless but also m = -1 and n = -1 so we get that length has inverse\nunits to mass... and so on.\n\nCan one do systematic units from a Lagrangian? Can opne the further\nderive the relationship to the SI units and the conversion constants\nfrom this picture? Has this been done somewhere?\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>And our descendants 200 years hence (historians of science excepted)
> might be blisfullly unaware that different units for space and time
> ever existed.
>
> But alas, the metric system came too early,
> and it is too late to change again,
>
Unlikely. The practical difference is just to great. For heat and
energy it doesn'tmatter. Energy is never meassured directly. distances
and times are, and with very different instruments.
Which is why, while in theoretical sciences it may make no conceptual
sense to treat them with different units it certainly makes a lot of
conceptual sense in experimental sciences where you have to treat them
very differently.
Therefore they are here to stay, therefore the confussion and the need
to translate them when going from a theoretically convenient system to
an experimentally convenient system.
That said, I still would like to get a reference that seriously
explains the theoretically convenient modelland systematically
explores the origin of units.
It always seemed to me that the reason why we only need one unit is
because the only important thing is how the individual variables
contribute to the Lagrangian which should be of [unit]^m.
So we can have m * v ^ 2 if [m] = [unit] and [length] = [time] =
[unit] ^ n and if we want to get the right units for the harmonic
potential m * x ^ 2 we get m = 2n + 1. We could have length and time
unitless but also m = -1 and n = -1 so we get that length has inverse
units to mass... and so on.
Can one do systematic units from a Lagrangian? Can opne the further
derive the relationship to the SI units and the conversion constants
from this picture? Has this been done somewhere?
Danny Ross Lunsford
Aug18-04, 09:59 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\nCerthas@gmail.com (Frank Hellmann) wrote in message\n\n> It always seemed to me that the reason why we only need one unit is\n> because the only important thing is how the individual variables\n> contribute to the Lagrangian which should be of [unit]^m.\n\nI think the actual reason here is the tacit assumption of globally\ninvariant scales, so one deals with tensors instead of tensor\ndensities.\n\ne.g. in Weyl\'s extension of Riemannian geometry, one deals with\nessential tensor densities everywhere, characterized by properties\nunder both coordinate and scale transformations, so sensible equations\nmust involve objects of the same weight - the geometry amounts to a\nkind of abstract dimensional analysis. An interesting thing would be\nto generalize this to more complex "units", that is, weights that are\nother than simple numbers. In such a thing the covariant derivative\nwould look like\n\nDm = dm + Nkm Akm\n\nmuch as in gauge theory.\n\n-drl\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Certhas@gmail.com (Frank Hellmann) wrote in message
> It always seemed to me that the reason why we only need one unit is
> because the only important thing is how the individual variables
> contribute to the Lagrangian which should be of [unit]^m.
I think the actual reason here is the tacit assumption of globally
invariant scales, so one deals with tensors instead of tensor
densities.
e.g. in Weyl's extension of Riemannian geometry, one deals with
essential tensor densities everywhere, characterized by properties
under both coordinate and scale transformations, so sensible equations
must involve objects of the same weight - the geometry amounts to a
kind of abstract dimensional analysis. An interesting thing would be
to generalize this to more complex "units", that is, weights that are
other than simple numbers. In such a thing the covariant derivative
would look like
Dm = dm + Nkm Akm
much as in gauge theory.
-drl
J. J. Lodder
Aug19-04, 04:51 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\nFrank Hellmann <Certhas@gmail.com> wrote:\n\n> > And our descendants 200 years hence (historians of science excepted)\n> > might be blisfullly unaware that different units for space and time\n> > ever existed.\n> >\n> > But alas, the metric system came too early,\n> > and it is too late to change again,\n> >\n>\n> Unlikely. The practical difference is just to great. For heat and\n> energy it doesn\'tmatter. Energy is never meassured directly. distances\n> and times are, and with very different instruments.\n\nLike a GPS and a GPS?\nAnd you are wrong:\nall distances are measured with a clock, ultimately.\nWhen you start asking how those marks on your metre rod\ncame to be where they are you end up at a clock\nin a standards laboratory.\n\n> Which is why, while in theoretical sciences it may make no conceptual\n> sense to treat them with different units it certainly makes a lot of\n> conceptual sense in experimental sciences where you have to treat them\n> very differently.\n> Therefore they are here to stay, therefore the confussion and the need\n> to translate them when going from a theoretically convenient system to\n> an experimentally convenient system.\n\nThe nanosecond would be a very practical unit of length\nfor everyday use. It equals about a foot.\nThe nano would be a very practical unit of speed.\nIt equals about 1 km/h\nThe only reason for not changing is backwards compatibility:\nThere is just too much that has been archived in metres,\nand the conversion factor 299 792 458 m/s is just too nasty.\n\nBut: were we still using Parisian toises, and Imperial inches,\ndifferent of course from US inches, etc. etc.,\nand only now changing over to new universal \'scientific\' units\nthere can be little doubt that there would not be\nan independent unit of length in the new system.\n\n> That said, I still would like to get a reference that seriously\n> explains the theoretically convenient modelland systematically\n> explores the origin of units.\n\nSearch under \'metrology\' for more than you can read.\n\n> It always seemed to me that the reason why we only need one unit is\n> because the only important thing is how the individual variables\n> contribute to the Lagrangian which should be of [unit]^m.\n> So we can have m * v ^ 2 if [m] = [unit] and [length] = [time] =\n> [unit] ^ n and if we want to get the right units for the harmonic\n> potential m * x ^ 2 we get m = 2n + 1. We could have length and time\n> unitless but also m = -1 and n = -1 so we get that length has inverse\n> units to mass... and so on.\n>\n> Can one do systematic units from a Lagrangian? Can opne the further\n> derive the relationship to the SI units and the conversion constants\n> from this picture? Has this been done somewhere?\n\nNo, Lagrangians and unit systems have nothing to do with each other.\nYou can write the Lagrangian in any unit system you want\nwithout changing the physical content of the theory it describes.\n\nJan\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Frank Hellmann <Certhas@gmail.com> wrote:
> > And our descendants 200 years hence (historians of science excepted)
> > might be blisfullly unaware that different units for space and time
> > ever existed.
> >
> > But alas, the metric system came too early,
> > and it is too late to change again,
> >
>
> Unlikely. The practical difference is just to great. For heat and
> energy it doesn'tmatter. Energy is never meassured directly. distances
> and times are, and with very different instruments.
Like a GPS and a GPS?
And you are wrong:
all distances are measured with a clock, ultimately.
When you start asking how those marks on your metre rod
came to be where they are you end up at a clock
in a standards laboratory.
> Which is why, while in theoretical sciences it may make no conceptual
> sense to treat them with different units it certainly makes a lot of
> conceptual sense in experimental sciences where you have to treat them
> very differently.
> Therefore they are here to stay, therefore the confussion and the need
> to translate them when going from a theoretically convenient system to
> an experimentally convenient system.
The nanosecond would be a very practical unit of length
for everyday use. It equals about a foot.
The nano would be a very practical unit of speed.
It equals about 1 km/h
The only reason for not changing is backwards compatibility:
There is just too much that has been archived in metres,
and the conversion factor 299 792 458 m/s is just too nasty.
But: were we still using Parisian toises, and Imperial inches,
different of course from US inches, etc. etc.,
and only now changing over to new universal 'scientific' units
there can be little doubt that there would not be
an independent unit of length in the new system.
> That said, I still would like to get a reference that seriously
> explains the theoretically convenient modelland systematically
> explores the origin of units.
Search under 'metrology' for more than you can read.
> It always seemed to me that the reason why we only need one unit is
> because the only important thing is how the individual variables
> contribute to the Lagrangian which should be of [unit]^m.
> So we can have m * v ^ 2 if [m] = [unit] and [length] = [time] =
> [unit] ^ n and if we want to get the right units for the harmonic
> potential m * x ^ 2 we get m = 2n + 1. We could have length and time
> unitless but also m = -1 and n = -1 so we get that length has inverse
> units to mass... and so on.
>
> Can one do systematic units from a Lagrangian? Can opne the further
> derive the relationship to the SI units and the conversion constants
> from this picture? Has this been done somewhere?
No, Lagrangians and unit systems have nothing to do with each other.
You can write the Lagrangian in any unit system you want
without changing the physical content of the theory it describes.
Jan
J. J. Lodder
Aug19-04, 04:51 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\nrobert bristow-johnson <rbj@surfglobal.net> wrote:\n\n> nospam@de-ster.demon.nl (J. J. Lodder) wrote in message news:<1gigomq.1kseudkc\nnww31N@de-ster.xs4all.nl>...\n> > Erik <erite423@yahoo.se> wrote:\n> >\n> > > et cetera. However, judging from Appendix F in R.M. Wald\'s "General\n> > > Relativity" or Appendix F in Burcham & Jobes\' "Nuclear and Particle\n> > > Physics", particle physicists and general relativists really do mean\n> > > exactly what they write.\n> >\n> > Of course, what else did you expect? This is physics.\n>\n> oh c\'mon Jan, physikers are never nebulous about the concepts they\n> deal with?? i\'m only a lowly EE but as we move from Newton through\n> Einstein, Heisenberg, Schrodinger, and on to quarks and eventually\n> strings, this thing gets more obscure by the minute (despite Green\'s\n> "Elegant Universe").\n\nThis is about units, remember?\nNo reason for nebulosity.\n(or even confusion)\n\n> > > Appendices like those discuss which\n> > > dimensions become equal when constants are set to unity. Thus, the\n> > > above equations really do mean that the entire physical constant, as\n> > > opposed to just its numerical value, is set to 1.\n> >\n> > Indeed, an often made choice is to have c = 1 and dimensionless.\n> >\n> > > Or so I thought until I, less than an hour ago, reread Duff, Okun &\n> > > Veneziano\'s discussion of how many truly fundamental constants there\n> > > are.\n> > > There, in section "5. The art of putting c = 1, hbar = 1, G = 1", L.B.\n> > > Okun claims that these expressions are not genuine equalities and that\n> > > they should not be taken too literally.\n> >\n> > Okun doesn\'t understand this game.\n>\n> but does he understand the *reality*? (as much as Duff and/or\n> Veneziano?)\n\nWhat is \'the reality\'?\n(please don\'t answer)\n\n> > > So what is the status of the above equations?\n> >\n> > They define a system of units.\n>\n> a system of units that are totally non-anthropocentric. that is a\n> very special system of units that, it seems to me, that Nature prefers\n> to express herself with.\n\n\'Nature\' is nobody, and has no preferences.\n\n> > > What do they really mean?\n> >\n> > They have no \'real\' meaning, beyond defining a unit system.\n> > Reality (by definition) doesn\'t depend on the unit system\n> > we -choose- to describe it with.\n>\n> but, apart from little dimensionless factors (like 4*pi, i still think\n> that Planck should have set 4*pi*G to 1, or perhaps 8*pi*G to 1) that\n> people get to argue about, it isn\'t *we* who choose these Natural\n> Units. it\'s Nature. *we* only get to discover them\n\nNo Platonic propaganda please.\n\n> > > Is Okun wrong?\n> >\n> > Yes.\n>\n> Jan, it\'s difficult for a slug (i.e. elec. engr.) like me to decide\n> who to believe. you? Okun? Baez? Duff? Veneziano? all\n> heavyweights.\n\nWhoever you want. It is only a matter of party lines,\nso you can freely choose which party you want to adhere to.\n\n> but Okun makes more natural sense to me on some stuff\n> (i actually go further and Duff would call me a "partisan of the\n> 4-Constant Party" because i see electric charge as a distinct\n> dimension of physical quantity apart from time, length, and mass) and\n> Duff on other stuff (such as our inability to detect a change in a\n> dimensionful constant since we always measure dimensionful quantities\n> against some other like dimensioned standard).\n\nNot surprised. You prefer to make the same mistakes.\n(believing in the objective reality of things like dimensions\nthat don\'t have an objective reality)\nThe mistake is not in: adhering to a party line,\nit is in believing that one particular party can be right, exclusively.\n\n> > > (I understand that constants can be made to disappear from fundamental\n> > > equations through clever changes of variables. E.g., a cleverly chosen\n> > > factor b will transform the Schrodinger equation for psi(x,t) to an\n> > > equation in terms of the field phi(s,t) = psi(bs,t). That equation\n> > > looks exactly like the simplified version of the Schrodinger equation\n> > > that could obtained if the equation m = e = hbar = 1 were taken\n> > > literally. Perhaps m = e = hbar = 1 is just the instruction "make the\n> > > changes of variables that make m, e, and hbar disappear!", rather than\n> > > a statement that m, e, and hbar are all equal to each other and to 1?\n> >\n> > That amounts to the same thing, in practice.\n>\n> that i understand (and agree with).\n>\n> > > But then it\'s difficult to make sense of Wald\'s appendix F and Burcham\n> > > & Jobes\' appendix F...)\n> >\n> > The key to understanding this subject is that dimensions\n> > do not have an objective existence.\n>\n> boy, that\'s an existential statement!! why can\'t the same be said of\n> any physical quantity?\n\nBecause measurement is the arbiter.\nWere you to claim for example that sound travels faster than light,\nand I the opposite, our friends could go through their motions,\nwith their rods and clocks, and decide who is right.\nWere you to claim that lenght and time must have different dimensions,\nand I that they must be the same,\nthen there is no way to decide which of us is right.\n(Actually there is, but it involves unpleasant means,\nlike burning opponents at the stake)\n\n> > They are human constructs,\n> > without relation to reality,\n>\n> is not any/every physical theory? we humans construct a theory to\n> attempt to describe what we observe (with whatever senses and\n> instruments we have) in what we think is reality. to say that force\n> or mass is really there but the fundamental differentiation between\n> quantities of time and length or mass or energy, that those\n> fundamental distictions of "stuff" are not really there but are merely\n> human constructs?? that\'s hard to swallow. (at least for engineering\n> slugs.)\n\nDescribing will do.\nThere is no need to invoke a \'reality\' behind the phenomena.\nWhat has objective meaning are those aspects of \'Nature\'\nthat do not depend on one particular way of describing it.\n\n> > to be chosen in any convenient way,\n> > subject only to the requirement of consistency.\n> > Any consistent system of dimensions is as good as any other,\n>\n> i think the jury is still out on that verdict.\n\nYou must be confusing it with the Central Commitee.\nBut is there a case, to begin with?\n\n> > although perhaps less useful for certain applications.\n>\n> that is true (at least IMHO).\n>\n> > In particular, one can give c value 1, and dimension [I],\n>\n> i dunno what [I] is.\n\nThe identity element of the dimension algebra,\ncorresponding to \'dimensionless\'.\nLike in a dimension formula such as [L] * [L]^{-1} = [I],\nor [I] * [L] = [L]\n\n> > or value 1, and dimension [L]/[T],\n> > whichever may be convenient for a particular application.\n>\n> dimension is important to help check on errors. if you end up adding\n> (or comparing) apples to oranges, it\'s a good idea to recheck your\n> maths. comparing(or summing) unlike dimensioned quantities is not\n> physically meaningful, at least to the neaderthal engineers.\n\nWhat has, or hasn\'t, the same dimension depends\non your system of dimensions.\nCan you add a metre to a second?\nIs \\hbar + c = 2 correct?\n\n> > A often used compromise is to have c = 1,\n> > and to write it nevertheless in final results,\n> > as in for example m_{top} = 175 GeV/c^2.\n>\n> i would think that once you set c=1, you better not stick it in later\n> lest you replace some "1" somewhere with the wrong power of c by not\n> keeping track of it.\n\nWould it really surprise you to learn that there are better ways?\nAfter all, a competent physist can compute anything you want\nin any unit system.\n\n> the way to keep track is to leave it in there\n> from the beginning. i mean, which is it? is it\n>\n> G(mu,nu) = 8*pi*G * T(mu,nu) ?\n>\n> or is it\n>\n> G(mu,nu) = 8*pi*G/c^4 * T(mu,nu) ?\n>\n> maybe it\'s c^3 or c^2?\n\nThe foolproof way to translate between unit systems automatically\n(even EE proof :-)\nis to set up the same system of dimensions for both.\n\n> sorry to be a thorn.\n\nDon\'t worry,\nI\'ve tried to explain these things to electrical engineers before,\n(without much succes, I\'m afraid)\n\nJan\n\n--\n"In my youth, young man, I took to the law,\nand argued each case with my wife.\nThe muscular strenth that gave to my jaw\nhas lasted the rest of my life." (Father William)\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>robert bristow-johnson <rbj@surfglobal.net> wrote:
> nospam@de-ster.demon.nl (J. J. Lodder) wrote in message news:<1gigomq.1kseudkc
nww31N@de-ster.xs4all.nl>...
> > Erik <erite423@yahoo.se> wrote:
> >
> > > et cetera. However, judging from Appendix F in R.M. Wald's "General
> > > Relativity" or Appendix F in Burcham & Jobes' "Nuclear and Particle
> > > Physics", particle physicists and general relativists really do mean
> > > exactly what they write.
> >
> > Of course, what else did you expect? This is physics.
>
> oh c'mon Jan, physikers are never nebulous about the concepts they
> deal with?? i'm only a lowly EE but as we move from Newton through
> Einstein, Heisenberg, Schrodinger, and on to quarks and eventually
> strings, this thing gets more obscure by the minute (despite Green's
> "Elegant Universe").
This is about units, remember?
No reason for nebulosity.
(or even confusion)
> > > Appendices like those discuss which
> > > dimensions become equal when constants are set to unity. Thus, the
> > > above equations really do mean that the entire physical constant, as
> > > opposed to just its numerical value, is set to 1.
> >
> > Indeed, an often made choice is to have c = 1 and dimensionless.
> >
> > > Or so I thought until I, less than an hour ago, reread Duff, Okun &
> > > Veneziano's discussion of how many truly fundamental constants there
> > > are.
> > > There, in section "5. The art of putting c = 1, \hbar = 1, G = 1", L.B.
> > > Okun claims that these expressions are not genuine equalities and that
> > > they should not be taken too literally.
> >
> > Okun doesn't understand this game.
>
> but does he understand the *reality*? (as much as Duff and/or
> Veneziano?)
What is 'the reality'?
(please don't answer)
> > > So what is the status of the above equations?
> >
> > They define a system of units.
>
> a system of units that are totally non-anthropocentric. that is a
> very special system of units that, it seems to me, that Nature prefers
> to express herself with.
'Nature' is nobody, and has no preferences.
> > > What do they really mean?
> >
> > They have no 'real' meaning, beyond defining a unit system.
> > Reality (by definition) doesn't depend on the unit system
> > we -choose- to describe it with.
>
> but, apart from little dimensionless factors (like 4*\pi, i still think
> that Planck should have set 4*\pi*G to 1, or perhaps 8*\pi*G to 1) that
> people get to argue about, it isn't *we* who choose these Natural
> Units. it's Nature. *we* only get to discover them
No Platonic propaganda please.
> > > Is Okun wrong?
> >
> > Yes.
>
> Jan, it's difficult for a slug (i.e. elec. engr.) like me to decide
> who to believe. you? Okun? Baez? Duff? Veneziano? all
> heavyweights.
Whoever you want. It is only a matter of party lines,
so you can freely choose which party you want to adhere to.
> but Okun makes more natural sense to me on some stuff
> (i actually go further and Duff would call me a "partisan of the
> 4-Constant Party" because i see electric charge as a distinct
> dimension of physical quantity apart from time, length, and mass) and
> Duff on other stuff (such as our inability to detect a change in a
> dimensionful constant since we always measure dimensionful quantities
> against some other like dimensioned standard).
Not surprised. You prefer to make the same mistakes.
(believing in the objective reality of things like dimensions
that don't have an objective reality)
The mistake is not in: adhering to a party line,
it is in believing that one particular party can be right, exclusively.
> > > (I understand that constants can be made to disappear from fundamental
> > > equations through clever changes of variables. E.g., a cleverly chosen
> > > factor b will transform the Schrodinger equation for \psi(x,t) to an
> > > equation in terms of the field \phi(s,t) = \psi(bs,t). That equation
> > > looks exactly like the simplified version of the Schrodinger equation
> > > that could obtained if the equation m = e = \hbar = 1 were taken
> > > literally. Perhaps m = e = \hbar = 1 is just the instruction "make the
> > > changes of variables that make m, e, and \hbar disappear!", rather than
> > > a statement that m, e, and \hbar are all equal to each other and to 1?
> >
> > That amounts to the same thing, in practice.
>
> that i understand (and agree with).
>
> > > But then it's difficult to make sense of Wald's appendix F and Burcham
> > > & Jobes' appendix F...)
> >
> > The key to understanding this subject is that dimensions
> > do not have an objective existence.
>
> boy, that's an existential statement!! why can't the same be said of
> any physical quantity?
Because measurement is the arbiter.
Were you to claim for example that sound travels faster than light,
and I the opposite, our friends could go through their motions,
with their rods and clocks, and decide who is right.
Were you to claim that lenght and time must have different dimensions,
and I that they must be the same,
then there is no way to decide which of us is right.
(Actually there is, but it involves unpleasant means,
like burning opponents at the stake)
> > They are human constructs,
> > without relation to reality,
>
> is not any/every physical theory? we humans construct a theory to
> attempt to describe what we observe (with whatever senses and
> instruments we have) in what we think is reality. to say that force
> or mass is really there but the fundamental differentiation between
> quantities of time and length or mass or energy, that those
> fundamental distictions of "stuff" are not really there but are merely
> human constructs?? that's hard to swallow. (at least for engineering
> slugs.)
Describing will do.
There is no need to invoke a 'reality' behind the phenomena.
What has objective meaning are those aspects of 'Nature'
that do not depend on one particular way of describing it.
> > to be chosen in any convenient way,
> > subject only to the requirement of consistency.
> > Any consistent system of dimensions is as good as any other,
>
> i think the jury is still out on that verdict.
You must be confusing it with the Central Commitee.
But is there a case, to begin with?
> > although perhaps less useful for certain applications.
>
> that is true (at least IMHO).
>
> > In particular, one can give c value 1, and dimension [I],
>
> i dunno what [I] is.
The identity element of the dimension algebra,
corresponding to 'dimensionless'.
Like in a dimension formula such as [L] * [L]^{-1} = [I],
or [I] * [L] = [L]
> > or value 1, and dimension [L]/[T],
> > whichever may be convenient for a particular application.
>
> dimension is important to help check on errors. if you end up adding
> (or comparing) apples to oranges, it's a good idea to recheck your
> maths. comparing(or summing) unlike dimensioned quantities is not
> physically meaningful, at least to the neaderthal engineers.
What has, or hasn't, the same dimension depends
on your system of dimensions.
Can you add a metre to a second?
Is \hbar + c = 2 correct?
> > A often used compromise is to have c = 1,
> > and to write it nevertheless in final results,
> > as in for example m_{top} = 175 GeV/c^2.
>
> i would think that once you set c=1, you better not stick it in later
> lest you replace some "1" somewhere with the wrong power of c by not
> keeping track of it.
Would it really surprise you to learn that there are better ways?
After all, a competent physist can compute anything you want
in any unit system.
> the way to keep track is to leave it in there
> from the beginning. i mean, which is it? is it
>
> G(\mu,\nu) = 8*\pi*G * T(\mu,\nu) ?
>
> or is it
>
> G(\mu,\nu) = 8*\pi*G/c^4 * T(\mu,\nu) ?
>
> maybe it's c^3 or c^2?
The foolproof way to translate between unit systems automatically
(even EE proof :-)
is to set up the same system of dimensions for both.
> sorry to be a thorn.
Don't worry,
I've tried to explain these things to electrical engineers before,
(without much succes, I'm afraid)
Jan
--
"In my youth, young man, I took to the law,
and argued each case with my wife.
The muscular strenth that gave to my jaw
has lasted the rest of my life." (Father William)
greywolf42
Aug20-04, 04:47 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n"J. J. Lodder" <nospam@de-ster.demon.nl> wrote in message\nnews:1gipqxl.blgmfm72alnwN@de-ster.xs4all.nl...\n>\n> Frank Hellmann <Certhas@gmail.com> wrote:\n>\n{snip}\n\n> all distances are measured with a clock, ultimately.\n> When you start asking how those marks on your metre rod\n> came to be where they are you end up at a clock\n> in a standards laboratory.\n\nOnly if you used a clock to make the marks. They didn\'t use clocks in the\nold days.\n\nThe redefinition of distance into a time multiplied by light speed was a\nvery recent change. And it is not necessary, merely a new convention.\n\n> > Which is why, while in theoretical sciences it may make no conceptual\n> > sense to treat them with different units it certainly makes a lot of\n> > conceptual sense in experimental sciences where you have to treat them\n> > very differently.\n> > Therefore they are here to stay, therefore the confussion and the need\n> > to translate them when going from a theoretically convenient system to\n> > an experimentally convenient system.\n>\n> The nanosecond would be a very practical unit of length\n> for everyday use. It equals about a foot.\n\nOnly at lightspeed. And lightspeed varies in the real world ... depending\nupon the local environment.\n\nOf course\n\n> The nano would be a very practical unit of speed.\n> It equals about 1 km/h\n\n\'Nano\' is a prefix of a unit (10^-9). It is not a unit itself. A unit of\nspeed would be nanosecond per second (or per nanosecond). Which -- to me --\nindicates that the attempt shows how confusing the whole effort would be.\n\n> The only reason for not changing is backwards compatibility:\n> There is just too much that has been archived in metres,\n\nThe whole point of the metric system was to make useful, descriptive set of\nunits of rational relationships. There are already metric units for time\n(tics are the equivalent of the second).\n\n> and the conversion factor 299 792 458 m/s is just too nasty.\n\nFar better than slugs, furlongs and feet.\n\n> But: were we still using Parisian toises, and Imperial inches,\n> different of course from US inches, etc. etc.,\n> and only now changing over to new universal \'scientific\' units\n> there can be little doubt that there would not be\n> an independent unit of length in the new system.\n\nThe history of the metric system is fascinating. Only the yanks retain\ninches. There is no \'US inch.\' It\'s an English inch. But I have heard\nthat the Brits went metric.\n\n{snip}\n\n--\ngreywolf42\nubi dubium ibi libertas\n{remove planet for e-mail}\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>"J. J. Lodder" <nospam@de-ster.demon.nl> wrote in message
news:1gipqxl.blgmfm72alnwN@de-ster.xs4all.nl...
>
> Frank Hellmann <Certhas@gmail.com> wrote:
>
{snip}
> all distances are measured with a clock, ultimately.
> When you start asking how those marks on your metre rod
> came to be where they are you end up at a clock
> in a standards laboratory.
Only if you used a clock to make the marks. They didn't use clocks in the
old days.
The redefinition of distance into a time multiplied by light speed was a
very recent change. And it is not necessary, merely a new convention.
> > Which is why, while in theoretical sciences it may make no conceptual
> > sense to treat them with different units it certainly makes a lot of
> > conceptual sense in experimental sciences where you have to treat them
> > very differently.
> > Therefore they are here to stay, therefore the confussion and the need
> > to translate them when going from a theoretically convenient system to
> > an experimentally convenient system.
>
> The nanosecond would be a very practical unit of length
> for everyday use. It equals about a foot.
Only at lightspeed. And lightspeed varies in the real world ... depending
upon the local environment.
Of course
> The nano would be a very practical unit of speed.
> It equals about 1 km/h
'Nano' is a prefix of a unit (10^-9). It is not a unit itself. A unit of
speed would be nanosecond per second (or per nanosecond). Which -- to me --
indicates that the attempt shows how confusing the whole effort would be.
> The only reason for not changing is backwards compatibility:
> There is just too much that has been archived in metres,
The whole point of the metric system was to make useful, descriptive set of
units of rational relationships. There are already metric units for time
(tics are the equivalent of the second).
> and the conversion factor 299 792 458 m/s is just too nasty.
Far better than slugs, furlongs and feet.
> But: were we still using Parisian toises, and Imperial inches,
> different of course from US inches, etc. etc.,
> and only now changing over to new universal 'scientific' units
> there can be little doubt that there would not be
> an independent unit of length in the new system.
The history of the metric system is fascinating. Only the yanks retain
inches. There is no 'US inch.' It's an English inch. But I have heard
that the Brits went metric.
{snip}
--
greywolf42
ubi dubium ibi libertas
{remove planet for e-mail}
J. J. Lodder
Aug24-04, 04:55 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>greywolf42 <mingstb@marssim-ss.com> wrote:\n\n> "J. J. Lodder" <nospam@de-ster.demon.nl> wrote in message\n> news:1gipqxl.blgmfm72alnwN@de-ster.xs4all.nl...\n> >\n> > Frank Hellmann <Certhas@gmail.com> wrote:\n> >\n> {snip}\n>\n> > all distances are measured with a clock, ultimately.\n> > When you start asking how those marks on your metre rod\n> > came to be where they are you end up at a clock\n> > in a standards laboratory.\n>\n> Only if you used a clock to make the marks. They didn\'t use clocks in the\n> old days.\n\nBut they didn\'t achieve 10^{-14} reproducibility either.\nThere is no stopping progress :-)\n\n> The redefinition of distance into a time multiplied by light speed was a\n> very recent change. And it is not necessary, merely a new convention.\n\nIt is absolutely necessary, and not merely a new convention,\nfrom a metrologists point of view.\nThe reason for it is not a desire theoretical neatness,\nbut an entirely practical one.\nThe metre based on the second can be reproduced more accurately\nthan any directly defined length standard.\n(by several orders of magnitude)\n-If- somebody were to invent a new length standard,\nreproducible to much better than 10^{-14}\nthe second would be abolished as an independent unit.\n\n> > > Which is why, while in theoretical sciences it may make no conceptual\n> > > sense to treat them with different units it certainly makes a lot of\n> > > conceptual sense in experimental sciences where you have to treat them\n> > > very differently.\n> > > Therefore they are here to stay, therefore the confussion and the need\n> > > to translate them when going from a theoretically convenient system to\n> > > an experimentally convenient system.\n> >\n> > The nanosecond would be a very practical unit of length\n> > for everyday use. It equals about a foot.\n>\n> Only at lightspeed. And lightspeed varies in the real world ... depending\n> upon the local environment.\n\nOf course not.\nA nanosecond is 0.299792458 m, exactly, and by definition.\n\n> Of course\n\n????? part of your sentence missing.\n\n> > The nano would be a very practical unit of speed.\n> > It equals about 1 km/h\n>\n> \'Nano\' is a prefix of a unit (10^-9). It is not a unit itself. A unit of\n> speed would be nanosecond per second (or per nanosecond). Which -- to me --\n> indicates that the attempt shows how confusing the whole effort would be.\n\nNo doubt some convenient name for \'10^{-9}\' could be invented.\nLacking an official definition I\'ll use \'nano\', if you don\'t mind.\nBTW, your objection is neither new nor original.\nOpposition to the metric system back in 1800 already focussed\non those queer and outlandisch or even \'barbaric\' prefixes,\nlike (then) \'hecto\'.\n\n> > The only reason for not changing is backwards compatibility:\n> > There is just too much that has been archived in metres,\n>\n> The whole point of the metric system was to make useful, descriptive set of\n> units of rational relationships. There are already metric units for time\n> (tics are the equivalent of the second).\n>\n> > and the conversion factor 299 792 458 m/s is just too nasty.\n>\n> Far better than slugs, furlongs and feet.\n>\n> > But: were we still using Parisian toises, and Imperial inches,\n> > different of course from US inches, etc. etc.,\n> > and only now changing over to new universal \'scientific\' units\n> > there can be little doubt that there would not be\n> > an independent unit of length in the new system.\n>\n> The history of the metric system is fascinating. Only the yanks retain\n> inches. There is no \'US inch.\' It\'s an English inch. But I have heard\n> that the Brits went metric.\n\nThere was a US inch. And it was different from the imperial inch.\nBoth were defined independently to 6+ decimal places.\nHowever, \'very recently\' it was decided to abolish all independent\ndefinitions of the non-metric units, and to redefine both the US inch\nand the imperial inch to be 25.4 mm (exactly).\nSo, the new inch is not equal to the old \'English\' inch.\nAnd indeed, the Brits -officially- went metric,\nso perhaps in another hundred years ...\n\nBest,\n\nJan\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>greywolf42 <mingstb@marssim-ss.com> wrote:
> "J. J. Lodder" <nospam@de-ster.demon.nl> wrote in message
> news:1gipqxl.blgmfm72alnwN@de-ster.xs4all.nl...
> >
> > Frank Hellmann <Certhas@gmail.com> wrote:
> >
> {snip}
>
> > all distances are measured with a clock, ultimately.
> > When you start asking how those marks on your metre rod
> > came to be where they are you end up at a clock
> > in a standards laboratory.
>
> Only if you used a clock to make the marks. They didn't use clocks in the
> old days.
But they didn't achieve 10^{-14} reproducibility either.
There is no stopping progress :-)
> The redefinition of distance into a time multiplied by light speed was a
> very recent change. And it is not necessary, merely a new convention.
It is absolutely necessary, and not merely a new convention,
from a metrologists point of view.
The reason for it is not a desire theoretical neatness,
but an entirely practical one.
The metre based on the second can be reproduced more accurately
than any directly defined length standard.
(by several orders of magnitude)
-If- somebody were to invent a new length standard,
reproducible to much better than 10^{-14}
the second would be abolished as an independent unit.
> > > Which is why, while in theoretical sciences it may make no conceptual
> > > sense to treat them with different units it certainly makes a lot of
> > > conceptual sense in experimental sciences where you have to treat them
> > > very differently.
> > > Therefore they are here to stay, therefore the confussion and the need
> > > to translate them when going from a theoretically convenient system to
> > > an experimentally convenient system.
> >
> > The nanosecond would be a very practical unit of length
> > for everyday use. It equals about a foot.
>
> Only at lightspeed. And lightspeed varies in the real world ... depending
> upon the local environment.
Of course not.
A nanosecond is .299792458 m, exactly, and by definition.
> Of course
????? part of your sentence missing.
> > The nano would be a very practical unit of speed.
> > It equals about 1 km/h
>
> 'Nano' is a prefix of a unit (10^-9). It is not a unit itself. A unit of
> speed would be nanosecond per second (or per nanosecond). Which -- to me --
> indicates that the attempt shows how confusing the whole effort would be.
No doubt some convenient name for '10^{-9}' could be invented.
Lacking an official definition I'll use 'nano', if you don't mind.
BTW, your objection is neither new nor original.
Opposition to the metric system back in 1800 already focussed
on those queer and outlandisch or even 'barbaric' prefixes,
like (then) 'hecto'.
> > The only reason for not changing is backwards compatibility:
> > There is just too much that has been archived in metres,
>
> The whole point of the metric system was to make useful, descriptive set of
> units of rational relationships. There are already metric units for time
> (tics are the equivalent of the second).
>
> > and the conversion factor 299 792 458 m/s is just too nasty.
>
> Far better than slugs, furlongs and feet.
>
> > But: were we still using Parisian toises, and Imperial inches,
> > different of course from US inches, etc. etc.,
> > and only now changing over to new universal 'scientific' units
> > there can be little doubt that there would not be
> > an independent unit of length in the new system.
>
> The history of the metric system is fascinating. Only the yanks retain
> inches. There is no 'US inch.' It's an English inch. But I have heard
> that the Brits went metric.
There was a US inch. And it was different from the imperial inch.
Both were defined independently to 6+ decimal places.
However, 'very recently' it was decided to abolish all independent
definitions of the non-metric units, and to redefine both the US inch
and the imperial inch to be 25.4 mm (exactly).
So, the new inch is not equal to the old 'English' inch.
And indeed, the Brits -officially- went metric,
so perhaps in another hundred years ...
Best,
Jan
Michael Mandelberg
Aug25-04, 02:44 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>I must admit that I am now confused. I thought I had understood this\nstuff some time ago, but maybe not. I remember that one standard\napplication of dimensional analysis is determining the period of a\npendulum. Given the mass of the bob, the length of the string, and the\nacceleration due to gravity, there is only one way to get a time:\n\nSqrt[ L/g ]\n\nTherefore the period is some constant times this, which is good in the\nsmall amplitude approximation. How would this analysis proceed in an\napproach with only one dimensional quantity?\n\nMichael Mandelberg\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>I must admit that I am now confused. I thought I had understood this
stuff some time ago, but maybe not. I remember that one standard
application of dimensional analysis is determining the period of a
pendulum. Given the mass of the bob, the length of the string, and the
acceleration due to gravity, there is only one way to get a time:
\Sqrt[ L/g ]
Therefore the period is some constant times this, which is good in the
small amplitude approximation. How would this analysis proceed in an
approach with only one dimensional quantity?
Michael Mandelberg
Cl.Massé
Aug28-04, 08:43 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\n"Michael Mandelberg" <mmandelberg@comcast.net> a écrit dans le message\nde news:144785.0408241115.d09f84d@posting.google.com. ..\n\n> I must admit that I am now confused. I thought I had understood this\n> stuff some time ago, but maybe not. I remember that one standard\n> application of dimensional analysis is determining the period of a\n> pendulum. Given the mass of the bob, the length of the string, and the\n> acceleration due to gravity, there is only one way to get a time:\n>\n> Sqrt[ L/g ]\n>\n> Therefore the period is some constant times this, which is good in the\n> small amplitude approximation. How would this analysis proceed in an\n> approach with only one dimensional quantity?\n\nThat\'s an example in classical mechanics, which requires several\ndimension in its very premises. But treated in modern theories,\nespecially quantum mechanics and general relativity, there are other\nways.\nActually, with general relativity we no longer have two mass dimensions.\nAn identification was already done on experimental basis, but without a\ntheoretical background.\n\n--\n~~~~ clmasse on free dot F-country\nLiberty, Equality, Profitability.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>"Michael Mandelberg" <mmandelberg@comcast.net> a écrit dans le message
de news:144785.0408241115.d09f84d@posting.google.com. ..
> I must admit that I am now confused. I thought I had understood this
> stuff some time ago, but maybe not. I remember that one standard
> application of dimensional analysis is determining the period of a
> pendulum. Given the mass of the bob, the length of the string, and the
> acceleration due to gravity, there is only one way to get a time:
>
> \Sqrt[ L/g ]
>
> Therefore the period is some constant times this, which is good in the
> small amplitude approximation. How would this analysis proceed in an
> approach with only one dimensional quantity?
That's an example in classical mechanics, which requires several
dimension in its very premises. But treated in modern theories,
especially quantum mechanics and general relativity, there are other
ways.
Actually, with general relativity we no longer have two mass dimensions.
An identification was already done on experimental basis, but without a
theoretical background.
--
~~~~ clmasse on free dot F-country
Liberty, Equality, Profitability.
J. J. Lodder
Aug30-04, 02:24 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Michael Mandelberg <mmandelberg@comcast.net> wrote:\n\n> I must admit that I am now confused. I thought I had understood this\n> stuff some time ago, but maybe not. I remember that one standard\n> application of dimensional analysis is determining the period of a\n> pendulum. Given the mass of the bob, the length of the string, and the\n> acceleration due to gravity, there is only one way to get a time:\n>\n> Sqrt[ L/g ]\n\nAssuming in addition that no other variables matter\nand that no fundamental constant (like c) creeps in,\nand that the result must be a power law.\n\n> Therefore the period is some constant times this, which is good in the\n> small amplitude approximation. How would this analysis proceed in an\n> approach with only one dimensional quantity?\n\nNot.\nTo draw conclusions when two physical quantities are involved\nyou need at least a two-dimensional algebra of dimensions.\n(sorry about the confusion in terminology: the choice of the word\n\'dimension\' was most unfortunate, but it is too late too change)\n\nUsing a one-dimensional system of dimensions\nbased on [T] for example (or equivalently [E] = [T]^{-1})\n[L] = [T], [g] = [T]^{-1},\nand you can only conclude that period = constant L^x g^{-1+x}\n\nFrom here you can still get the answer by using an order of magnitude\nestimate; since both l and g are very small O(10^{-9}),\nwhile T must be O(1), x must be 1/2.\nA more rigorous approach is to use a richer dimensional algebra,\nfor example the usual MLT one.\n\nAs mentioned before, the key is to note\nthat values and dimensions have in principle\nnothing do do with each other:\nyou can give c the value 299 792 458 and dimension 1,\nor the value 1 and dimension [L]/[T],\nif that suits your needs.\n\nBest,\n\nJan\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Michael Mandelberg <mmandelberg@comcast.net> wrote:
> I must admit that I am now confused. I thought I had understood this
> stuff some time ago, but maybe not. I remember that one standard
> application of dimensional analysis is determining the period of a
> pendulum. Given the mass of the bob, the length of the string, and the
> acceleration due to gravity, there is only one way to get a time:
>
> \Sqrt[ L/g ]
Assuming in addition that no other variables matter
and that no fundamental constant (like c) creeps in,
and that the result must be a power law.
> Therefore the period is some constant times this, which is good in the
> small amplitude approximation. How would this analysis proceed in an
> approach with only one dimensional quantity?
Not.
To draw conclusions when two physical quantities are involved
you need at least a two-dimensional algebra of dimensions.
(sorry about the confusion in terminology: the choice of the word
'dimension' was most unfortunate, but it is too late too change)
Using a one-dimensional system of dimensions
based on [T] for example (or equivalently [E] = [T]^{-1})
[L] = [T], [g] = [T]^{-1},
and you can only conclude that period = constant L^x g^{-1+x}
From here you can still get the answer by using an order of magnitude
estimate; since both l and g are very small O(10^{-9}),
while T must be O(1), x must be 1/2.
A more rigorous approach is to use a richer dimensional algebra,
for example the usual MLT one.
As mentioned before, the key is to note
that values and dimensions have in principle
nothing do do with each other:
you can give c the value 299 792 458 and dimension 1,
or the value 1 and dimension [L]/[T],
if that suits your needs.
Best,
Jan
Gerard Westendorp
Aug31-04, 02:40 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>In the thread "Solitons in one post", Tessel explained that\ndimensional analyses is just an example of the more general\nconcept of symmetry.\n\nThis is maybe an interesting way to look at it.\nSuppose you have a physical model, with variables (x,y,..).\nx and y are measured in certain units. We could have chosen\nother units. In that case, we would obtain a new set of\nnumbers (x,y,..) -> (X,Y,..). All laws of physics must\nstill be valid in these new units.\nIn other words, a change of units is a symmetry operation\nthat leaves the laws of physics invariant.\n\nSo, what are the Noether currents (conserved quantities)\nassociated with these symmetries?\n\nI haven\'t yet figured out the answer, so someone might want\nto beat me to it.\n\nGerard\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>In the thread "Solitons in one post", Tessel explained that
dimensional analyses is just an example of the more general
concept of symmetry.
This is maybe an interesting way to look at it.
Suppose you have a physical model, with variables (x,y,..).
x and y are measured in certain units. We could have chosen
other units. In that case, we would obtain a new set of
numbers (x,y,..) -> (X,Y,..). All laws of physics must
still be valid in these new units.
In other words, a change of units is a symmetry operation
that leaves the laws of physics invariant.
So, what are the Noether currents (conserved quantities)
associated with these symmetries?
I haven't yet figured out the answer, so someone might want
to beat me to it.
Gerard
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